---

We give a precise example of a polynomial vector feld on $mathbb{R}^2$ whose corresponding singular holomorphic foliation of $mathbb{C}^2$ possesses a complex limit cycle which does not intersect the real plane $mathbb{R}^2$.

---

 In this paper we give a topology-dynamical interpretation for the space  of all integer sequences $P_n$ whose consecutive difference $P_{n+1}-P_n$ is a bounded sequence.  We also introduce a new concept textit{"Rigid Banach space"}. A rigid  Banach space is a Banach space $X$  such that for  every continuous linear injection $j:Xto X,;overline{J(X)}$ is either isomorphic to $X$ or it does not contain any isometric copy of $X$. We prove that $ell_{infty}$ is not a rigid Banach space. We also  discuss about  rigidity of Banach algebras.